As a medic, (it's really the only class I feel comfortable commenting on), the most important thing, 9 times out of 10, is to survive. Every little bit of ubercharge you lose from death in the end will make your job harder.. so run around, trying to keep everyone topped up, use your medigun's targeting mechanics to keep yourself as out of the fight as possible, preferably tucked around a corner. The simplest and usually best match for a medic is the heavy but depending on the medigun you're using, you might be better off focusing on something else.
A standard Uber is cake for a Heavy if you have to break a point filled with enemies, whereas a better use for your Uber might be a soldier or demo if you need to break an engineer pillbox. Other gun Ubers though have different priorities. Kritzkrieg Soldier is simply amazing, and if you're using a Quick Fix (which I don't suggest unless you're really good at switching targets in a heated fight), the priorities are almost swapped - suddenly the pyro and scout are great picks because of their enhanced speed and low HP (you can overheal a Heavy by 150hp but a scout at full overheal is increased by 30). another thing about the Quick Fix that's not mentioned in the description is that if you're healing a rocket/grenade jumper, you also get launched along with them, into the air. So if you're really good, a great Soldier/Medic or Demo/Medic team can absolutely destroy.
Another tip could be try to keep your back to a wall whenever possible. Your biggest enemies will be Spies. But if they can't effectively backstab you, they're easy enough to deal with. Other major enemies are Pyros, but there's a certain combination of weapons (I think it's the Crusaders Crossbow and the Amputator) that gives you an additional 1hp per second. This combo makes pyros a lot easier to deal with, because the hp/sec overwrites a lot of the Pyro's residual damage, so if they're skirmishing pyros, you won't have nearly as much trouble with them (also a lot less scrambling for medkits and a lot less TOTAL OVERWHELMING RAGE when other players pick them up when you're right there in pain). Pyros will still annihilate you in a straight fight, but their residual flames (which are the Medic's second worst enemy) will be lessened.
If you're pugging without voice chat, you need to get a feeling for when to Uber. Lots of people complain about medics cooking their ubers (sort of like cooking grenades if you know the expression), but once you get a bit more skilled, you'll get a sense for how much ammo your target has used, and know when to Uber. I don't like to Uber until my healing isn't cutting it. I've had far too many moments where I Uber too early and bad things happen. It's a very short buff and I like to use it to its fullest when I can. Ideally, you'll pair up with someone and get to know them, and then you can figure out the best ways to use your abilities. Best Case scenario, you're playing with a friend in the same room.
On the flipside, you don't want to have 100% uber for very long, so once you get an Uber, find a place to use it, and then hopefully, survive the fight and live to Uber again. A lot of rough nights getting backstabbed with full Uber. Bad times. Also remember that you can't Uber yourself and then switch weapons and go all super rambo - switching weapons will immediately cancel the Uber. And remember that in a pinch, the medic IS capable of going super rambo. The Overdrive is really the best weapon for it, but they also have some great melee weapons. I'm fairly certain the bonesaw is basically the most powerful out of the box melee weapon, except the backstab of course. Other weapons are slightly less punchy, but have interesting powers, the only one I have no use for is the Amputator (except when dealing with pyros as mentioned above). I love the Vita-Saw as it allows you to retain uber after dying and pairs well with the quickfix and overdrive which allows you to be a crazy zipping super rambo bastard.
I'm rambling now, and you might not even want to play medic, and heck, I'm a total scrub so I could be giving you COMpLETELY wrong advice. I just know how I play.
